Thursday, July 12, 2007

The mice clamored for actual examples of pressure broadened lines and how well they could be fit. This is a fairly specialized area, and papers appear in a very small number of journals, principally the Journal of Quantitative Spectroscopy and Radiative Transfer, the Journal of Molecular Spectroscopy, Molecular Physics and Applied Optics. Eli went and downloaded some papers from JQSRT about line broadening in CO2.

These are two examples from a diode laser spectrum of L. Joly, et al., "A complete study of CO2 line parameters around 4845 cm-1 for Lidar applications. JQSRT (2007), doi:10.1016/j.jqsrt.2007.06.003. The spectrum and the fit are shown in the top panels the residuals are shown in the bottom two panels for Voigt and Rautian profiles respectively. In this case the Rautian is better than the Voigt. In both cases the P12 line of the (201) Note the different scales on the frequency axes. The scale for the spectrum on the right is four times larger than for that on the left. UPDATE: The full width at half maximum (FWHM) of the line on the right is about four times larger than that on the left. The x-axis scales in the two graphs are different.

Next we can look at an example from V. Malathy Devia, D. Chris Benner, M.A.H. Smith, and C.P. Rinsland, "Nitrogen broadening and shift coefficients in the 4.2–4.5-m bands of CO2" JQSRT 76 (2003) 289–307 showing 20 calculated spectra (bottom panel) and the residuals between the calculated and observed spectra (upper panel). This includes self broadening and broadening due to N2. The cell has a mixture of 12C and 13C CO2. In this case Voigt profiles were used. The largest line is P(30) for the 12CO2 (001) The broadening depends on the rotational quantum number, the and the pressure. Details can be found in the paper and are included in HITRAN.

UPDATE: If you want to learn about temperature effects see here and for more on pressure broadening see here and here

Sorry, but I wasn't really nitpicking, at least not in the sense of looking for missing periods.

If you are measuring the width of the line, you generally use the divisions below the line, right? Isn't that the whole point in putting them there in the first place?

So, if someone is measuring the widths of absorption lines on different graphs (using the divisions below each graph) , you want to remind them that the divisions represent different amounts by telling them they are scaled differently.

It's not clear why you would compare the total spans along the bottom because people generally use the divisions for the measurement. At least I do (but maybe I'm just weird).

But I do agree it's not a topic for deep conversation.

Sorry I brought it up. It won't happen again. I promise.

So, now, where were we?

Ah yes, talking about important matters like high school honors papers.

Marion, Voigt is as you say a combination of a Gaussian and a Lorentzian profile. In the impact approximation (infinitely short time binary collisions) you can show that pressure broadening is described by a Lorentzian. If you relax this condition and assume that there are a range of impact parameters (how close the collision partners get) and velocities (determines the time of the collision) you can do a more sophisticated analysis. Since the collisions now change the velocity of the emitter this also screws up the description of the Doppler profile as a simple Gaussian. At some point it becomes a question of how much pain you want to accept. Rautian-Sobelman is another level you can google it.

Self-Broadening would be broadening by collisions with the same molecule, e.g. CO2 broadening caused by other CO2 molecules.

'At some point it becomes a question of how much pain you want to accept."

yes indeed

If i am not mistaken, impact broadening, self-broadening and pressure broadening are all examples of what is known in spectroscopy circles as hammer broadening" named after the famous nobel winning physicist I.F. Ida Hammer.

note that most of the absorption takes place in the red region of the spectrum and that the full width at half max is actually grater than that at 1/10 max

The Lorentizan line shape can be dervied from a simple classical model. Model the vibrating, rotating molecule as a dipole oscillator. The absorption spectrum of an ensemble of such oscillators is the Fourier Transform of the Dipole correlation function. You can envisage this function by imagining that you start all of the oscillators off with the same phase. Collisions interrupt the phase of the oscillators. In the impact limit, the phase of the oscillator after the collision is entirely uncorrelated with its phase before the collision - in other words, the molecule retains no memory of it prior phase. That leads directly to an exponentially decaying correlation function (molecules are removed from the ensemble of in-phase oscillators at random times) with a decay constant proportional to the collision rate. And the Fourier Transform of an exponential is a Lorentzian.

Effectively Hansen has. You can find most of his stuff at the GISS site and also at his Columbia web site, including most of his presentations. Increasingly government agencies are requiring that publications from their labs be openly available on the net.

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Eli Rabett

Eli Rabett is a not quite failed professorial techno-bunny, a chair election from retirement, at a wanna be research university that has a lot to be proud of but has swallowed the Kool-Aid. The students are naive but great and the administrators vary day-to-day between homicidal and delusional. His colleagues are smart, but they have a curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they occasionally heed his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.